Léa Cot (LATTIS, Université de Toulouse)

« Séance ouverture » : Estimation of chaotic map parameters

vendredi 22 janvier 2010, 9h30 - 10h45

Salle de réunion, espace Turing

The LATTIS laboratory from the University of Toulouse has developed a digital chaos-based
cryptosystem. The objective of this project is to estimate the map parameters from which the
chaotic signals result.

Chaotic signals may be generated by nonlinear two-dimensional maps depending on parameters.
Because of the high sensitivity of chaos to initial condition, by slightly modifying the initial
conditions, sequences with similar distributions can be generated, but will never take the same

Moreover, chaotic signals are similar to random noise and may be used to conceal information and
encipher transmission by mixing them with the message in an appropriate manner.
Consequently, chaotic sequences may be used to improve the security of transmissions. But this
supposes to be immune against potential attacks. We suppose that the chaotic map is known but not
the parameters. Because the exact values of the initial conditions and the parameters are unknown, a
hacker cannot reconstruct the chaotic sequences and decipher the message. He may therefore try to
estimate the map parameters using various techniques.
Two approaches have been considered to estimate the map parameters knowing only sequences
generated by this map.

On one hand, the Gauss-Newton method has been implemented in Matlab using directly the
sequences generated by a two dimensional chaotic map. It has also been tested by making an index
shift of sequence terms so that no transmission of consecutive terms occurs and the complexity in
estimation of parameter values is increased. Various chaotic maps have been tested.

On the other hand, the Extended Kalman Filter (EKF) method has been implemented and tested in
exactly the same conditions as the Gauss-Newton method.

This first approach of the estimation of chaotic map parameters shows Gauss Newton method seems
to be more efficient than Extended Kalman Filter. But, we are realizing complementary tests to
understand these results and to improve performance of EKF method for index shift problem.